Question

factorise the following x²-x-90 ​

Answer 1

Answer:

$= x^{2} - 10x + 9x - 90 \\ = x(x - 10) + 9(x - 10) \\ = (x + 9)(x -10) \\ = x = - 9 \: \: \: or \: x = 10$

Answer 2

The first term is,  x2  its coefficient is  1 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -90  

Step-1 : Multiply the coefficient of the first term by the constant   1*-90 = -90  

Step-2 : Find two factors of  -90  whose sum equals the coefficient of the middle term, which is   -1 .

     -90    +   1   =    -89  

     -45    +   2    =   -43  

     -30    +   3    =   -27  

     -18    +   5    =   -13  

     -15    +   6    =   -9  

     -10    +   9    =   -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  9  

                    x2 - 10x + 9x - 90

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x*(x-10)

             Add up the last 2 terms, pulling out common factors :

                   9*(x-10)

Step-5 : Add up the four terms of step 4 :

                   (x+9)*(x-10)

            Which is the desired factorization

Final result :

 (x + 9)*(x - 10)